Absolute Value Functions

The exploration is carried out by changing the parameters a, b and c included in f(x) above.

Interactive Tutorial

a =

-10+10

b =

-10+10

c =

-10+10

>

click on the button above "draw" to start.

Use the sliders to set parameter a to zero, parameter b to zero and parameter c to a positive value; f(x)is a constant function. Compare the graph of f(x) in blue and that of h(x) = |f(x)| in red. Change c to a negative value and compare the graphs again. Use the definition of the absolute value functions to explain how can the graph of |f(x)| be obtained from the graph of f(x).

Keep the value of a equal to zero, select non zero values for b to obtain a linear function . How can the graph of h(x) be obtained from that of f(x)?

Set b and c to zero and select a positive value for a to obtain a quadratic function . Why are the two graphs the same? (Hint: use the definition of the absolute value functions).

Set b and c to zero and select a negative value for a to obtain a quadratic function . Why are the two graphs reflection of each other? (Hint: use the definition of the absolute value functions and reflection of a graph on the x-axis).

Keep the values of a and b as in 5 above and change gradually c from zero to some positive values. How can the graph of h(x) be obtained from that of f(x)?

Select different values for a, b and c and explore.

Exercises
Sketch the following functions

f(x) = x - 1 and h(x) = |f(x)|

f(x) = x2 - 4 and h(x) = |f(x)|

f(x) = -x and h(x) = |f(x)|

You will find more pages in this web site related to absolute value functions and equations.